2 point charges are located at the coordinates in the figure, how much work needs to
move a point charge q = �]20ƒÊC from B to A?
link to photo
dropbox/s/x93u73xu2zslfqj/Untitled.png?dl=0
To determine the work needed to move a point charge from point B to point A, we need to calculate the electric potential difference between the two points.
The electric potential difference (ΔV) between two points is given by the equation:
ΔV = Vf - Vi
First, we need to calculate the electric potential (V) at each point. Electric potential is a scalar quantity that depends on the distance from the charged particles.
To calculate the electric potential at each point, we use the equation:
V = k * (q / r), where k is the electric constant (9 * 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the charged particle.
Using the given coordinates in the figure, we find that point A is at (-0.2 m, 0), and point B is at (0.2 m, 0).
Let's assume the point charge q is positive, and the two charges in the figure are negative to attract the point charge q towards point A.
Using the distance formula, we calculate the distances between the charges and each point:
Distance between charge 1 and point A (r1A) = sqrt((-0.2 - 0)^2 + (0 - 0)^2)
Distance between charge 1 and point B (r1B) = sqrt((0.2 - 0)^2 + (0 - 0)^2)
Distance between charge 2 and point A (r2A) = sqrt((-0.1 - 0)^2 + (0 - 0)^2)
Distance between charge 2 and point B (r2B) = sqrt((0.1 - 0)^2 + (0 - 0)^2)
Now, we can calculate the electric potentials at points A and B using the formula mentioned earlier.
Electric potential at point A (VA) = k * (q1 / r1A) + k * (q2 / r2A)
Electric potential at point B (VB) = k * (q1 / r1B) + k * (q2 / r2B)
Substitute the given charges and distances into the formulas to calculate the electric potentials.
Once you have obtained the electric potentials at points A and B, you can find the electric potential difference (ΔV) by subtracting VB from VA.
Finally, the work (W) needed to move the point charge q from point B to point A is given by the equation:
W = q * ΔV
Substitute the charge q and the electric potential difference ΔV into the formula to find the work needed.